Probabilistic Thinking — Monte Carlo Analysis
Precisely defining risk is a key requirement in ensuring better decision making. Frequently risks are ambiguously communicated — often with no more detail than as being high, medium or low. These terms can be interpreted very differently by stakeholders and leave no sense as to the spread of risk as inevitable swings in the outcome of assumptions cumulatively results in very different project outcomes. It is far more valuable to stakeholders to be able to communicate the risk probabilistically, for example there is a 70% chance the the project will return above the threshold 10% cost of capital hurdle and a 5% chance that it will lose money. One method of developing this probabilistic presentation of risk can be through using the Monte Carlo method of analysis.
Monte Carlo simulation uses repeated random sampling to simulate data for a given mathematical model and evaluate the outcome. This method was initially applied back in the 1940s, when scientists working on the atomic bomb used it to calculate the probabilities of one fissioning uranium atom causing a fission reaction in another. With uranium in short supply, there was little room for experimental trial and error. The scientists discovered that as long as they created enough simulated data, they could compute reliable probabilities — and reduce the amount of uranium needed for testing.
This method takes the likely range of inputs and randomly assigns possible outcomes for each input according to a pre-defined distribution. Then it combines the inputs per a mathematical formula to produce the required output of interest (profitability, project time, part dimension, quality etc). By completing this calculation many thousands (or even millions!) of times, the model is able to produce a distribution of outcomes on which to base your risk analysis.
Monte Carlo is pretty good [for risk analysis] because if you run 10,000 simulations and a particular outcome never occurs, your degree of belief in that outcome happening in the real world should be no more than around 10−4.
Monte Carlo is a:
brute-force approach made possible with computers. We randomly pick a bunch of exact values — thousands — according to the ranges we prescribed and compute a large number of exact values.
The Monte Carlo simulation is an excellent method for solving this problem. We would have to randomly generate values within the stated ranges, put them into the annual savings formula, and compute a result.
This is what we mean by ‘‘risk analysis.’’ We have to be able to compute the odds of various levels of losses. If you are truly measuring risk, this is what you can do. “How to Measure Anything” — Douglas W Hubbard
Monte Carlo analysis can be completed using Excel (either directly in Excel or with VBA (or here) ), Minitab, or other proprietary tools such as @Risk.
Monte Carlo analysis can also be used for estimating solutions to problems that are too complicated to solve directly through equations. A simple example of this it to estimate the value of PI by taking the ratio of dots that fall randomly in either a circle or square of radius 1.
Brian Christian and Tom Griffiths in their book “Algorithms to Live By” highlight the broader use of Monte Carlo in the computer sciences :
A close examination of random samples can be one of the effective means of making sense of something too complex to be comprehended directly. When it comes to handling a qualitatively unmanageable problem, something so thorny and complicated that it can’t be digested whole — solitaire or atomic fission, primality testing or public policy — sampling offers one of the simplest, and also the best, ways of cutting through the difficulties.
To summarise again the four steps for completing a Monte Carlo analysis:
- Identify a mathematical model of the activity or process you want to explore.
- Define the parameters (like mean and standard deviation) for each factor in your model.
- Create random data according to those parameters.
- Simulate and analyze the output of your process.
Completing these steps will improve the communication of risk into specific terms that are tangible to stakeholders. Of course like any model you have to be careful with the quality of your inputs however this will improve with practice and reflection.
